Furthermore, via email I contacted Victor Stenger and asked him about the quote. He then contacted Alexander Vilenkin and others about this claim by Craig. I feel very privileged to have had a very small part in the correspondence with these scientists. During the discussions Mr. Vilenkin explains how, yes, the theorem does prove that the universe had a beginning, however, this conclusion is not written in stone. Given various "subtleties" the theorem could be negated.
Mr. Stenger asked Mr. Vilenkin the following question,
Does your theorem prove that the universe must have had a beginning?
Vilenkin replied,
No. But it proves that the expansion of the universe must have had a beginning. You can evade the theorem by postulating that the universe was contracting prior to some time.
Vilenkin added,
This sounds as if there is nothing wrong with having contraction prior to expansion. But the problem is that a contracting universe is highly unstable. Small perturbations would cause it to develop all sorts of messy singularities, so it would never make it to the expanding phase. That is why Aguirre & Gratton and Carroll & Chen had to assume that the arrow of time changes at t = 0. This makes the moment t = 0 rather special. I would say no less special than a true beginning of the universe. [3]
In a follow up email to me Mr. Vilenkin made his position clearer,
[I]f someone asks me whether or not the theorem I proved with Borde and Guth implies that the universe had a beginning, I would say that the short answer is "yes". If you are willing to get into subtleties, then the answer is "No, but..." So, there are ways to get around having a beginning, but then you are forced to have something nearly as special as a beginning.
I further learned that the cyclic model of the universe (that I often propose by Paul Steinhardt and Neil Turok, authors of Endless Universe: Beyond the Big Bang), according to Vilenkin, "cannot be a complete description of the universe" because "[i]n the model of Steinhardt and Turok, there are some particles whose histories can be extended to the infinite past. Such particles go through an infinite succession of expansion and contraction cycles. But, as our theorem requires, histories of most particles cannot be so extended and should reach the boundary beyond which the cyclic picture no longer applies."